All this guy did was attempt to obtain free recognition to which he was not entitled; no different from somebody claiming to be a SEAL or wearing an unearned Silver Star.
In the case of this guy in New York, the impersonation charge would only apply if he impersonated someone to secure a financial or material advantage that should only have been accorded to the person or type of person he was impersonating. Unless the airline in question had a specific -- and publicly documented -- policy of upgrading active-duty military personnel to first class, then the guy committed no crime. The fact that a well-meaning pilot, flight attendant or other airline representative offered to upgrade him to first class simply on the basis of his uniform doesn't make him a criminal.
It's important to remember that in cases like this, the prosecutor has to show that someone suffered harm or financial loss due to the alleged impersonation. Without such a legal standard in place, the police could legitimately walk through every shopping mall in American next December and arrest thousands of men for "impersonating" a guy named Santa Claus.